PHILO 11 X1 GROUP III (CLASS #: 11-14) MIDTERM EXAM ANSWERS 1.Let S = Plato went to Syracuse Let A = Alcibiades stayed in Athens Let R = Aristotle went to Rome Argument Form: S v A R v A -R S Truth Tree The argument was found to be consistent and invalid. The possible set of truth-values to provide the invalid proof is: T for A F for S F for R 2.Let M = Smith gave Brown the money Let W = Smith welshed on his bet Argument Form: -M ! W M -W Truth Tree: The argument was found to be consistent and invalid. The possible set of truth-values to provide the invalid proof is: T for M T for W 1S v A ! 2R v A ! 3--R 4-S From 5SA1 ! 6RA2 ! 1-M ! W ! 2M3--W !From 4W3 5 6 --M M W1 5 3.Let A = The Achaean fleet will be able to sail to Troy Let I = Agamemnon slays his daughter Iphigeneia Let C = Agamemnon will be killed by his wife Clytemnestra Argument Form: -A ! -I I ! C A C Truth Tree: The argument was found to be consistent and invalid. The possible set of truth-values to provide the invalid proof is: T for A F for I F for C 4.Let C = Angelo is in the circus Let K = Angelo is a clown Let W = Angelo is whimsical Argument Form: C v -K W v -C K ! W Truth Tree: The argument was found to be inconsistent and valid. All the branches were closed. 1-A ! -I !2I ! C ! 3A 4-C From 5--A !-I1 6A5 7-IC-IC2

! ! 1C v K ! 2W v C ! 3-(K ! W) !From 4K3 5-W3 6C-K1 ! 7W-C2 !! 5.Let C = Jesse Owens suffered leg cramps during the race Let W = Jesse Owens won the race Argument Form: -(C & W) W -C Truth Tree: The argument was found to be inconsistent and valid. All the branches were closed. 6.Let W = Filbert read War and Peace Let A = Filbert read Anna Karenina Let K = Ludmilla read Anna Karenina Let Z = Ludmilla read Doctor Zhivago Argument Form: W v A -K v Z K & -A W & Z Truth Tree: The argument was found to be inconsistent and valid. All the branches were closed. 1-(C & W) ! 2W3--C !From 4C3 5-C-W1 !! 1W v A ! 2-K v Z ! 3K & -A ! 4-(W & Z) !From 5K3 6-A3 7WA 1 ! 8-K Z2 ! 9 -W-Z4 !! 7.Let L = Lagos is the capital of Nigeria Let A = Accra is the capital of Nigeria Let G = Lagos is the capital of Ghana Let C = Accra is the capital of Ghana Argument Form: L v A G v C A v C L v G Truth Tree: The argument was found to be consistent and invalid. The possible set of truth-values to provide the invalid proof is: T for A T for C F for L F for G . 8.Let H = Hitler will attack Russia Let L = Luftwaffe gains control of the skies over England Let O = Germany launches Operation Sea Lion Argument Form: H v (L & O) -L H Truth Tree: The argument was found to be inconsistent and valid. All the branches were closed. 1L v A ! 2G v C ! 3A v C !4-(L v G) !From 5-L4 6-G4 7LA 1 ! 8GC2 ! 9 AC3 1H v (L & O) ! 2-L 3-HFrom 4H(L & O) !1 5 6 ! O L ! 4 4 9.Let G = Milhous graduates Let J = Milhous takes a jobLet A = Milhous goes into the army Argument Form: G ! (J v A) G -J ! A Truth Tree: The argument was found to be inconsistent and valid. All the branches were closed. 10.Let L = Bob is looking Let C = Ernie cheats at croquet Let M = Ernie takes another martini Let B = Ernie has a glass of beer Let W = Ernie wins at croquet Argument Form:Truth Tree: -L ! (C v M) (B & W) ! -M -C ! -W The argument was found to be consistent and invalid. The possible set of truth-values to provide the invalid proof is: T for L T for W F for C F for B F for M 1G ! (J v A) ! 2G 3-(-J ! A) !From 4-J3 5-A3 6-G(J v A) !1 ! 7JA6 !! 1-L ! (C v M) ! 2(B & W) ! -M ! 3-(-C ! -W) !From 4-C3 5--W3 W5 6-(B & W) !-M2 7-B-W ! 6 8 9 --L ! L (C v M) !--L ! L (C v M) !1 8 10C ! M ! C ! M ! 8 11.Let P = Tai will defeat Petrosian Let F = Tai will defeat Fischer Let K = Tais opening move is with the kings pawnLet M = Fisher has the first move Argument Form:Truth Tree: (P & F) "! K-F ! M M K ! P The argument was found to be inconsistent and valid. All the branches were closed. 12.Let T = Professor Mumble will give a testLet C = The class has covered ten chaptersLet L = Professor Mumble lost his lecture notes Let D = Professor Mumble had too much to drink at the Faculty Club after class Argument Form:Truth Tree: -(C v L) ! -T -D ! -L (C & D) ! T The argument was found to be consistent and invalid. The possible set of truth-values to provide the invalid proof is: T for C T for D F for T Either T or F for L 1(P & F) "! K ! 2-F ! M 3-M4-(K ! P) !From 5K4 -P4 6(P & F) & K !-(P & F) & -K !1 7 8 9 (P&F) !P F ! -K ! 6 7 7 1-(C v L) ! -T ! 2-D ! -L ! 3-[(C & D) ! T] !From 4(C&D) !3 5-T3 6C4 7D4 8--(C v L) !-T 1 9(C v L) !8 10CL9 11 12 --D !D-L--D ! D -L ! --D ! D -L2 12 13.Let C = Sherlock Holmes caught the criminal Let L = Dr. Watson is lying Let I = Sherlock Holmes correctly identified the cigar ash Argument Form: C v L -I ! C L v C Truth Tree: The argument was found to be inconsistent and valid. All the branches were closed. 14.Let Q = The gods quarrel Let J = The gods quarrel over what is just and good Let P = Anyone is pleased by what he thinks just and good Let D = Anyone is displeased by what he thinks unjust and bad Let O = One thing can please one god Let A = One thing can displease another god Argument Form: Truth Tree: Q Q ! J P & D J ! (O & A) (O & A) The argument was found to be inconsistent and valid. All the branches were closed. 1C v L ! 2-I ! C 3-(L v C) !From 4-L3 -C 5CL1 !! 1Q 2Q ! J ! 3P & D ! 4J ! (O & A) ! 5-(O& A) !From 6P3 7D3 8-Q ! J2 9 10 11 -J ! (O & A) ! O A 4 9 9 12-O ! -A ! 7 15.Let G = Lady Chatterly will meet the game-keeper Let I = Clifford is impotent Let V = Lady Chatterly does go to Venice Argument Form: -(I & -V) ! -G V -G Truth Tree: The argument was found to be inconsistent and valid. All the branches were closed. 16.Let A = God is able to prevent evil Let O = God is omnipotent Let W = God is willing to prevent evil Let B = God is benevolent Let E = Evil exists Let G = God exists Argument Form:Truth Tree: -A ! -O (A & -W) ! -B -(-W v A) ! -E E G ! (O & B) -G The argument was found to be inconsistent and valid. All the branches were closed. 1-(I & -V) ! -G ! 2V 3--G !From 4G3 5 6 7 8 --(I & -V)(I & -V) I V ! -G ! 1 5 6 6 1 A ! -O ! 2(A & W) ! B ! 3(W v A) ! E ! 4E5G !(O & B) ! 6G !From7G 6 8 9 -G ! (O & B)O 5 8 10B8 8 11(W v A) !-E3 12(W v A) !!11 13WA12 14(A & W) !B(A & W) !B2 ! ! 15 16 A W!W ! AW! W 14 15 17AOAOAO1 !! !!!! 17.Let S = The social security system will succeed Let M = More money will be collected through social security taxes Let T = Many senior citizens will be in trouble Let C = Both members of Congress claim to be sympathetic to senior citizens Argument Form: M ! S S v T C & -M -S Truth Tree: The argument was found to be consistent and invalid. The possible set of truth-values to provide the invalid proof is: T for S T for T T for C F for M 18.Let A = The President acts quickly Let S = The social security system will be saved Let D = The senior citizens will be delighted Let M = The President is pressured by members of the Senate Let H = The President is pressured by members of the House Let C = The President is pressured by the senior citizens Argument Form:Truth Tree: (-S ! -A) & (S ! D) [(M v H) v C] ! A -(M v H) & C D The argument was found to be inconsistent and valid. All the branches were closed. 1M ! S ! 2S v T ! 3C & -M! 4--S !From 5S4 6C3 7-M3 8-MS 1

9STST2 1(-S ! -A) & (S ! D) ! 2[(M v H) v C] ! A ! 3-(M v H) & C ! From 4-D 5-(M v H)3 6C3 7-S ! -A !1 8S ! D !1 9 10 --S ! S -A7 9 11-S! D ! 8 12-[(M v H) v C] ! A2 13 -(M v H) !12 14-C12 !